Concern is growing for the welfare of James Cornforth, 36, who left the Ocean Terminal Shopping Centre shortly after 3pm on Tuesday, February 5.
Police have gone door-to-door and have been trawling CCTV in an effort to plot James’ movements.
Dad Martin Cornforth said: “It has now been a month since I last saw or spoke to James and along with his wife and the rest of the family we are all worried for his safety.
“This is completely out of character for him. James, if you read this, we just want to know that you are safe, please get in touch with someone as soon as possible.”
Officers have painstakingly pieced together his journey west on Tuesday, February 5 but the trail goes cold shortly after 8pm.
CCTV footage confirmed he left the Tesco Express store on Queensferry Road at around 5.40pm that day.
He passed the Shell garage on Maybury Road, before continuing west on foot towards Edinburgh Gateway and continued west and crossed the foot bridge over the A8 towards the RBS buildings at 6.32pm. Officers have now released fresh CCTV footage to show the last confirmed sighting of James at 8.01pm in the BP garage on Glasgow Road.
He bought a selection of food before leaving the store, heading west in the direction of Newbridge on foot.
He has not been in contact with anyone since.
James is around 5ft 10ins tall, of stocky build with short light-brown hair.
He has a sleeve tattoo on his right arm and a thistle tattoo on his right ankle.
He was last seen wearing a grey hoodie and blue jeans, and was carrying a dark-coloured rucksack.
Inspector Jonny Elliott from Drylaw Police Station said: “James’s family and friends are understandably upset by his disappearance and this is made harder as the weeks pass by.
“There have been no confirmed sightings of James since Tuesday 5 February.
“I would remind the public that the weather that night was poor with periods of heavy rain, with James walking over four miles between the Tesco on Queensferry Road and the BP garage on Glasgow Road.
“I’d urge anyone who saw James walking this route, or who may have seen him after he left the BP garage in the Ratho Station or Newbridge areas, to come forward at their earliest opportunity to assist with our investigation.
“In addition, any motorists, cyclists, lorry drivers or bus drivers who may have been recording via dash cam and who were using any part of the route we know James took along the A8 corridor, or in the Newbridge area, on Tuesday 5 February from 6pm onwards, are urged to come forward and provide this as soon as possible.”
Those with information can contact Police Scotland on 101, quoting incident number 1134 of February 7.